Find the equation of the linear function represented by the table below in slopeintercept form. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-1 & 2 \\ \hline 1 & 6 \\ \hline 3 & 10 \\ \hline 5 & 14 \\ \hline \end{tabular}
Solution
Step 1 ：The equation of a linear function is given by the formula \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 ：The slope can be calculated by taking the difference in y-values divided by the difference in x-values between any two points.
Step 3 ：Let's take two points from the table, point1 = (-1, 2) and point2 = (1, 6).
Step 4 ：Calculate the slope: \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 2}{1 - (-1)} = 2.0\). So, the slope of the line is 2.
Step 5 ：The y-intercept can be found by substituting the slope and one of the points into the equation and solving for \(b\).
Step 6 ：Substitute the slope and point1 into the equation: \(2 = 2*(-1) + b\). Solving for \(b\), we get \(b = 4.0\). So, the y-intercept is 4.
Step 7 ：Therefore, the equation of the line is \(y = 2x + 4\).
Step 8 ：Final Answer: The equation of the line is \(\boxed{y = 2x + 4}\).
